Finite Group Databasebeta

C2×#22562288 #31010215

order17152
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC2×#22562288

Splittings

SylowC67 ⋊ C2×#2214

Subgroups

subgroupG/H
centerC22#16863589
commutator, cosocleC2×C8×C67C24
FrattiniC2×C8C23×D67
FittingC2×#510×C67C2
socleC22×C67#459
prime radicalC2×#135×C67C22
hypercenterC2×#510D67
hypocenterC67C2×#2214
LCSG ▷ C2×C8×C67 ▷ C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#510

686 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4288

Conjugacy classes & character table

1102 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 323952);